In wireless communication systems, multiple antennas can be used for improving link reliability and/or increasing transmission rate. Multiple antenna techniques can be categorized on the basis of the availability of channel state information at a transmitter in two groups: an open loop mode and a closed loop.
In case of a closed loop mode transmission, pre-coding can be used to improve performance of a multiple antenna system.
In practice, feedback bandwidth constraint, feedback delay and channel estimation errors may cause channel state information at a transmitter, which is based on feedback information, being imperfect. For such cases, a transmitter and a receiver may have a common pre-coding codebook, i.e. a finite collection of pre-coding vectors (codewords). The receiver typically decides which vector or vectors of the codebook are selected for use and feedbacks its index to a transmitter via a feedback channel. Another possibility is that the transmitter decides which vector or vectors of the codebook are selected for its data transmission and signals its index to a receiver in order to allow data detection at the receiver end.
Several prior art codebooks are presented. Some of them are shown in D. J. Love and R. W. Heath, “Grassmannian beamforming for multiple-input multiple-output wireless systems”, IEEE Transactions on Information Theory, vol. 49, No. 10, pp. 2735-2747, October 2003; B. M. Hochwald, T. L. Marzetta, T. J. Richardson, W. Sweldens and R. Urbanke, “Systematic Design of Unitary Space-Time Constellations”, IEEE Transactions on Information Theory, vol. 46, No. 6, pp. 1962-1973, September 2000 and Intel et al., “Compact Codebooks for Transmit Beamforming in Closed-Loop MIMO”, IEEE C802.16e-05/050r6, which are taken herein as a reference.
However, a problem is that they usually do not provide good performance in different channel conditions, for example, some of them are good only in weakly correlated channels, whereas others are good only in strongly correlated channels.